.mn-calc-section { margin-bottom: 25px; padding: 15px; background: #f9f9f9; border-radius: 8px; }
.mn-calc-title { color: #2c3e50; font-size: 24px; font-weight: 700; margin-bottom: 20px; text-align: center; }
.mn-calc-row { display: flex; flex-wrap: wrap; gap: 15px; align-items: flex-end; margin-bottom: 10px; }
.mn-calc-input-group { flex: 1; min-width: 80px; }
.mn-calc-label { display: block; font-size: 13px; font-weight: 600; margin-bottom: 5px; color: #555; }
.mn-calc-input { width: 100%; padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; box-sizing: border-box; }
.mn-calc-btn { width: 100%; padding: 15px; background-color: #27ae60; color: white; border: none; border-radius: 6px; font-size: 18px; font-weight: 600; cursor: pointer; transition: background 0.3s; margin-top: 10px; }
.mn-calc-btn:hover { background-color: #219150; }
.mn-calc-result { margin-top: 25px; padding: 20px; background-color: #e8f6ef; border-radius: 8px; border-left: 5px solid #27ae60; display: none; }
.mn-calc-result-title { font-weight: bold; font-size: 18px; margin-bottom: 10px; color: #1e7e34; }
.mn-calc-math { font-family: "Courier New", Courier, monospace; font-size: 15px; margin-top: 10px; line-height: 1.6; }
.mn-calc-article { margin-top: 40px; line-height: 1.8; color: #444; }
.mn-calc-article h2 { color: #2c3e50; border-bottom: 2px solid #eee; padding-bottom: 10px; }
.mn-calc-article h3 { color: #34495e; margin-top: 25px; }
.mn-calc-fraction-ui { display: flex; align-items: center; gap: 5px; }
.mn-calc-fraction-v { display: flex; flex-direction: column; align-items: center; }
.mn-calc-fraction-line { border-top: 2px solid #333; width: 100%; margin: 2px 0; }
.mn-calc-input-small { width: 45px; text-align: center; padding: 5px; border: 1px solid #ccc; border-radius: 4px; }
@media (max-width: 600px) { .mn-calc-row { flex-direction: column; align-items: stretch; } }
function calculateUnitRate() {
var w1 = parseFloat(document.getElementById('w1').value) || 0;
var n1 = parseFloat(document.getElementById('n1').value) || 0;
var d1 = parseFloat(document.getElementById('d1').value) || 1;
var l1 = document.getElementById('l1').value || "units";
var w2 = parseFloat(document.getElementById('w2').value) || 0;
var n2 = parseFloat(document.getElementById('n2').value) || 0;
var d2 = parseFloat(document.getElementById('d2').value) || 1;
var l2 = document.getElementById('l2').value || "units";
if (d1 === 0 || d2 === 0) {
alert("Denominator cannot be zero.");
return;
}
// Convert Mixed to Improper: (W * D + N) / D
var improperNum1 = (w1 * d1) + n1;
var improperDen1 = d1;
var improperNum2 = (w2 * d2) + n2;
var improperDen2 = d2;
if (improperNum2 === 0) {
alert("The divisor quantity cannot be zero.");
return;
}
// Division: (A/B) / (C/D) = (A * D) / (B * C)
var finalNum = improperNum1 * improperDen2;
var finalDen = improperDen1 * improperNum2;
var decimalResult = finalNum / finalDen;
// Simplify Fraction
function getGCD(a, b) {
return b ? getGCD(b, a % b) : a;
}
var common = Math.abs(getGCD(finalNum, finalDen));
var simplifiedNum = finalNum / common;
var simplifiedDen = finalDen / common;
// Display Results
var resultArea = document.getElementById('mn-result-area');
var resultSummary = document.getElementById('mn-result-summary');
var stepByStep = document.getElementById('mn-step-by-step');
resultArea.style.display = "block";
var unitLabel = l1 + " per " + l2.replace(/s$/, ""); // Simple singularization attempt
resultSummary.innerHTML = decimalResult.toLocaleString(undefined, {maximumFractionDigits: 4}) + " " + unitLabel;
var steps = "Step 1: Convert to improper fractions";
steps += "Quantity 1: " + improperNum1 + "/" + improperDen1 + "";
steps += "Quantity 2: " + improperNum2 + "/" + improperDen2 + "";
steps += "Step 2: Divide fractions (Multiply by Reciprocal)";
steps += "(" + improperNum1 + "/" + improperDen1 + ") × (" + improperDen2 + "/" + improperNum2 + ")";
steps += "Step 3: Simplify";
steps += "Fraction: " + simplifiedNum + "/" + simplifiedDen + "";
steps += "Decimal: " + decimalResult.toFixed(4);
stepByStep.innerHTML = steps;
resultArea.scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}
Mixed Number Unit Rate Calculator
Whole Number
Numerator
Denominator
Label (e.g., Miles)
Whole Number
Numerator
Denominator
Label (e.g., Hours)
Calculation Result
Understanding Mixed Number Unit Rates
A unit rate is a comparison of two different quantities where the second quantity is reduced to one. When dealing with real-world measurements—like running 5 ½ miles in ¾ of an hour—we often encounter mixed numbers. A mixed number consists of a whole number and a proper fraction.
The Formula for Unit Rate
To find the unit rate from mixed numbers, you divide the first quantity by the second:
Unit Rate = (Quantity A) ÷ (Quantity B)
Step-by-Step Calculation Process
- Convert Mixed Numbers to Improper Fractions: Multiply the whole number by the denominator and add the numerator. Place this over the original denominator.
- Apply Division Logic: To divide fractions, multiply the first fraction by the reciprocal (the flipped version) of the second fraction.
- Simplify: Multiply the numerators together and the denominators together, then simplify the resulting fraction or convert it to a decimal.
Example Calculation
Imagine a chef uses 2 ½ cups of flour to make 1 ¼ batches of cookies. What is the unit rate (flour per batch)?
- Convert: 2 ½ = 5/2. 1 ¼ = 5/4.
- Divide: 5/2 ÷ 5/4 = 5/2 × 4/5.
- Solve: (5 × 4) / (2 × 5) = 20 / 10 = 2.
- Result: 2 cups of flour per batch.